Hair Sticking Through Face
You are using interpolated children. Those try to place children between hair strands. Simplest case: The hair closest to the current hair has a deformation slightly different than the original, if a child is placed half way between them, it will have a 50:50 mix between both positions and deformations. That can easily cause bad results, especially when 2 hairs are fairly close together, but combed in the opposite direction, the interpolation can look like what you're seeing. For longer hair simple children are usually the better option.